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The short answer is no, since the package versions of optional packages are hardcoded into each Sagemath version, so that the behaviour is predictible.

So if you want to have normaliz 3.8.0 (or 3.8.1) installed within Sage, before some Sage release proposes it, you will have to modify SAGE_DIR/build/pkgs/normaliz/package-version.txt and SAGE_DIR/build/pkgs/normaliz/checksums.ini yourself. See for more details.

If this is beyond your skills and you need some feature that exists in 3.8.0 and not 3.7.2, please tell us, and i (or some other developer) will update the package quickly.